# A Novel EPANET Integration for the Diffusive–Dispersive Transport of Contaminants

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study

#### 2.2. EPANET-DD Model

^{3}/h) and the diameter of each pipeline, calculating and iterating the uniform flow rate to coincide with the measured flow rate upstream of the network. Numerous experimental tests were conducted on the network, varying the pressure set at the pumping system (3.5–4.5 bar) and the flow rates drawn from the network nodes (between 5 and 15 L/min for nodes 5, 8 and 11).

^{2}) [19].

^{2}) measures the goodness of fit of a statistical model. It is defined as the squared value of the linear correlation coefficient. The R

^{2}value ranges between 0 and 1. A value of zero indicates that there is no correlation between the two data series. On the other hand, higher coefficient values indicate a better fit for the model. However, it is not always true that large R

^{2}values result in a good model fit, as the linear correlation coefficient could produce a perfectly positive or negative relationship [19].

## 3. Results and Discussion

^{2}, graphically, there is no correspondence between the simulated and measured data to justify these values. As shown in Figure 2, this model worked well only for one node of the network (Figure 2a), which is supported by a high value of the KGE, NSE and R

^{2}coefficients reported in Table 6. This node, directly downstream of the node where sodium chloride was injected, was characterised by a turbulent flow regime with a Reynolds number of 4112. Under these conditions, the advective model could centre the contamination’s peak and the time interval in which it occurred, despite having a higher peak concentration. Analysing the remaining nodes shown in Figure 2b–f, the advective model reproduced anticipated events concerning the experimental data, which in some cases corresponded to a few minutes. Still, in the case of Figure 2c, the event was expected for approximately an hour. Furthermore, as shown in Figure 2c,d, the model underestimated the persistence of the contamination, as the event was quickly exhausted.

^{2}than that calculated for the other nodes. In this node, the coexistence of the transition and laminar flow regimes, which had Reynolds values of 3598 and 200, respectively, was observed. The transition flow regime most likely dominated because the dispersive effects were not overpowering. Furthermore, the model could centre the contamination peak for the node above despite having overestimated its mass.

^{2}coefficient values, as shown in Table 6. In fact, for all the monitored nodes in Figure 2, the model could centre the contamination peak. Furthermore, considering Figure 2b,f, which have transition flow regimes with Reynolds numbers of 3598, the model perfectly fits the experimental data departing from the classic bell-shaped trend typical of a Gaussian distribution. It is worth noting that at node 9 in Figure 2d, which has a laminar flow regime with a Reynolds number of 514, the model perfectly fits the ascending branch of the experimental data but failed to reproduce the descending limb of the curve. This is due to a separation between the contamination behaviour at the edge and the centre of the pipeline caused by the transition from turbulent to laminar flow. For the previous node, in Figure 2e, the model had a gap with the experimental data in the descending part of the curve but perfectly reproduced the terminal part of the pollutograph.

## 4. Conclusions

^{2}). Two other models (the advective model EPANET and an advective-dispersive model based on the formulations of Romero-Gomez and Choi) were evaluated concerning the experimental data, and the performance of the new model was compared with the results obtained from the advective model.

- The advective model works well only in locations close to the contamination node, where it can intercept the contamination’s peak even for lower values. In fact, relatively high values of the KGE, NSE and R
^{2}coefficients were observed at node 6 near the contamination node (0.44, 0.52, 0.29 respectively). - In all other cases, the contamination event was anticipated and had a shorter duration than that detected by the experimental campaign. As a result, much lower or even negative values of the three coefficients were obtained.
- The Romero-Gomez and Choi model can represent the dispersive behaviour of the contaminant. Still, it poorly represents the experimental data regarding delay or anticipation of the contamination peak and overestimating the contaminant mass. This was confirmed by the coefficients KGE, NSE, R
^{2}which resulted in some nodes (6, 7, 9, 10) being worse than those obtained using the advective model. - The new EPANET-DD model produced the best results in terms of adaptability with the experimental data. It simultaneously represented the peak time and provided better accuracy than the Romero-Gomez and Choi model. In fact, the coefficients considered were very high and, in some cases, close to unity.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The layout of the water distribution network (

**a**), overview of the water distribution network (

**b**), pumping system (

**c**), recirculation system (

**d**), installation of the pump-reservoir system (

**e**) and connection to the node (

**f**).

**Figure 2.**Comparison between experimental and simulated data using the three models (advective, Romero-Gomez and Choi (2011) [11] (backwards coefficient = 0.17, forwards coefficient = 0.51), EPANET-DD (backwards coefficient = 0.17, forwards coefficient = 0.51)) for a contamination event lasting 3 h subject to a network pressure of 1.5 bar for nodes 6 (

**a**), 7 (

**b**), 8 (

**c**), 9 (

**d**), 10 (

**e**), 11 (

**f**), obtained by contaminating node 5.

Functions | Descriptions |
---|---|

getLinkVelocity | Current computed flow velocity (read only) |

getLinkFlows | Current computed flow rate (read only) |

getLinkHeadloss | Current computed head loss (read only) |

getNodeHydaulicHead | Retrieves the computed values of all hydraulic heads |

getNodeActualDemand | Retrieves the computed value of all actual demands |

getNodePressure | Retrieves the computed values of all node pressures |

**Table 2.**Standard deviation between the pressures measured in the network and simulated numerically.

Node 6 | Node 7 | Node 9 | Node 10 | |
---|---|---|---|---|

σ [mH_{2}O] | 0.01 | 0.15 | 0.05 | 0.09 |

**Table 3.**Pipes roughness and standard deviation between the flow rates measured in the network and simulated numerically.

Link 5 | Link 6 | Link 7 | Link 9 | Link 10 | Link 11 | Link 13 | |
---|---|---|---|---|---|---|---|

Roughness [mm] | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

σ [m^{3}/h] | 0.12 | 0.12 | 0.08 | 0.11 | 0.11 | 0.11 | 0.15 |

**Table 4.**Standard deviation between the measured tapped flow rates and the numerically simulated flow rates.

Node 5 | Node 8 | Node 11 | |
---|---|---|---|

σ [L/min] | 0.45 | 0.07 | 0.07 |

Link 4 | Link 6 | Link 7 | Link 9 | Link 10 | Link 11 | Link 12 | Link 13 | |
---|---|---|---|---|---|---|---|---|

Reynolds (Re) | 4112 | 200 | 3598 | 1542 | 514 | 2056 | 1542 | 3598 |

Flow regime | Turbulent | Laminar | Transition | Laminar | Laminar | Transition | Laminar | Transition |

**Table 6.**Comparison of statistical parameters (Kling–Gupta efficiency, Nash–Sutcliffe efficiency, R

^{2}) for the advective, Romero-Gomez and Choi (2011) and EPANET-DD models.

Node | Advective Model | Romero-Gomez and Choi (2011) Model | EPANET-DD Model | ||||||
---|---|---|---|---|---|---|---|---|---|

KGE | NSE | R^{2} | KGE | NSE | R^{2} | KGE | NSE | R^{2} | |

6 | 0.44 | 0.52 | 0.29 | −0.60 | −0.72 | 0.21 | 0.63 | 0.69 | 0.49 |

7 | 0.25 | 0.59 | 0.68 | −0.08 | −0.15 | 0.12 | 0.81 | 0.84 | 0.76 |

8 | −0.55 | −1.50 | 0.08 | 0.01 | 0.35 | 0.04 | 0.45 | 0.43 | 0.92 |

9 | 0.22 | 0.18 | 0.43 | −1.58 | −5.57 | 0.13 | 0.29 | 0.35 | 0.17 |

10 | 0.34 | −0.01 | 0.19 | −4.35 | −14.81 | 0.09 | −0.15 | −0.54 | 0.55 |

11 | −0.30 | −0.62 | 0.05 | −0.94 | −1.18 | 0.79 | 0.42 | 0.76 | 0.90 |

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**MDPI and ACS Style**

Piazza, S.; Sambito, M.; Freni, G. A Novel EPANET Integration for the Diffusive–Dispersive Transport of Contaminants. *Water* **2022**, *14*, 2707.
https://doi.org/10.3390/w14172707

**AMA Style**

Piazza S, Sambito M, Freni G. A Novel EPANET Integration for the Diffusive–Dispersive Transport of Contaminants. *Water*. 2022; 14(17):2707.
https://doi.org/10.3390/w14172707

**Chicago/Turabian Style**

Piazza, Stefania, Mariacrocetta Sambito, and Gabriele Freni. 2022. "A Novel EPANET Integration for the Diffusive–Dispersive Transport of Contaminants" *Water* 14, no. 17: 2707.
https://doi.org/10.3390/w14172707